严格双对角占优矩阵的Schur补的双对角占优度及其应用  

Double Diagonally Dominant Degree of Schur Complement of the Strictly Double Diagonally Dominant Matrix and Its Application

作　　者：王金辉 李耀堂[1] WANG Jinhui;LI Yaotang(School of Mathematics and Statistics,Yunnan University,Kunming 650500)

机构地区：[1]云南大学数学与统计学院,昆明650500

出　　处：《工程数学学报》2024年第4期595-608,共14页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金(11861077).

摘　　要：矩阵Schur补是矩阵理论及其应用中的一个重要内容,具有广泛的应用背景。严格双对角占优矩阵是一类十分重要的特殊矩阵,流体力学的计算、材料模拟与设计、电磁场计算等领域与其有着密不可分的联系。对严格双对角占优矩阵的研究主要集中在两个方面:严格双对角占优矩阵的Schur补的特征值定位;严格双对角占优矩阵Schur补的逆的无穷范数估计。首先,给出了严格双对角占优矩阵的Schur补的双对角占优度的新下界估计式;然后,利用所给估计式获得了严格双对角占优矩阵Schur补新的特征值包含集和严格对角占优矩阵Schur补的逆的无穷范数的新上界。数值例子表明所获结果改进了一些现有结果。Matrix Schur complement is an important part of matrix theory and its application,which has a wide application background.Strictly double diagonally dominant matrices are a very important class of special matrices,which are closely related to uid mechanics calculation,material simulation and design,electromagnetic eld calculation and so on.The study of strictly double diagonally dominant matrices mainly focuses on two aspects:eigenvalue localization of Schur complement of strictly double diagonally dominant matrices;In nite norm estimation of inverse of Schur complement of strictly double diagonally dominant matrices.First,a new lower bound estimation of the double diagonally dominant degree of Schur complement of strictly double diagonally dominant matrices is given.Then,the new eigenvalue inclusion set of Schur complement of strictly double diagonally dominant matrices and the new upper bound of in nite norm for the inverse of Schur complement of strictly diagonally dominant matrices are obtained by using the obtained estimations.Numerical examples show that the results obtained in this paper improve some existing results.

关 键 词：双对角占优矩阵 双对角占优度 SCHUR补 特征值 

分 类 号：O24[理学—计算数学]